Existence of free boundary constant mean curvature disks

Início: 12/05/2023 17:00

Término: 12/05/2023 18:00

Palestrante: Da Rong Cheng (University of Miami)

E-mail do Palestrante: darong.cheng@miami.edu

Resumo: Given a surface S in R3, a classical problem is to find disk-type surfaces with prescribed constant mean curvature whose boundary meets S orthogonally. When S is diffeomorphic to a sphere, direct minimization could lead to trivial solutions and hence min-max constructions are needed. Among the earliest such constructions is the work of Struwe, who produced the desired free boundary CMC disks for almost every mean curvature value up to that of the smallest round sphere enclosing S. In a previous joint work with Xin Zhou (Cornell), we combined Struwe's method with other techniques to obtain an analogous result for CMC 2-spheres in Riemannian 3-spheres and were able to remove the "almost every" restriction in the presence of positive ambient curvature. In this talk, I will report on more recent progress where the ideas in that work are applied back to the free boundary problem to refine and improve Struwe's result.